📚 Year 9 WJEC Statistics: In-depth Analysis of Past Papers | Year 9 WJEC 统计：历年真题深度解析
Welcome to our detailed revision guide that breaks down real WJEC Year 9 Statistics past-paper questions. We examine essential topics, highlight typical mistakes, and provide clear, step-by-step solutions. Use this resource to strengthen your understanding and boost your exam confidence.
欢迎阅读这份深度复习指南，我们将拆解真实的 WJEC Year 9 统计历年真题。文章梳理核心主题，点出典型错误，并提供清晰的逐步解题方案。借助本资源巩固理解、提升应试信心。
1. Data Collection and Questionnaire Design | 数据收集与问卷设计
In WJEC past papers, you are frequently asked to critique a survey question and rewrite it in an unbiased form. A common task is to identify loaded questions, overlapping response boxes, or missing options.
在 WJEC 历年试卷中，经常要求你评判调查问题并以无偏形式重写。常见任务是识别引导性问题、重叠的回答选项或遗漏的选项。
Sample question: “A supermarket wants to find out how much customers enjoy their shopping experience. The questionnaire asks: ‘How much do you love our excellent fresh produce?’ with response boxes: Very much, A lot, Quite a bit.”
真题示例： “一家超市想了解顾客对购物体验的喜爱程度。问卷问道：’你有多喜爱我们优质的新鲜农产品？’ 选项为：非常喜欢、很喜欢、有点喜欢。”
The question is biased because it uses positive words like ‘love’ and ‘excellent’. It also lacks a neutral or negative option, such as ‘Not at all’ or ‘Dislike’. A better question would be: “How would you rate the freshness of our produce?” with options ranging from ‘Very good’ to ‘Very poor’.
该问题有偏，因为它使用了“喜爱”和“优质”等积极词语，且缺少中立或负面选项，如“一点也不”或“不喜欢”。更好的问法为：“你如何评价我们农产品的鲜度？” 选项范围从“非常好”到“非常差”。
Always ensure response boxes are exhaustive and mutually exclusive. Avoid double-barrelled questions and ambiguous wording. In the exam, you receive marks for clearly explaining why the original question is biased and for writing an improved version.
始终确保回答选项穷尽且互斥。避免双重问题和含糊措辞。考试中，清晰解释原问题为何有偏并写出改进版本即可获得分数。
2. Sampling Methods | 抽样方法
WJEC often tests your ability to select and justify a sampling method. You may need to describe how to obtain a simple random sample, a systematic sample, or a stratified sample from a given population.
WJEC 常考查你选择和解释抽样方法的能力。你可能需要描述如何从给定总体中获取简单随机样本、系统样本或分层样本。
Example: “A headteacher wants to survey 50 of the 800 students in a school. Describe how to take a stratified sample based on year groups.” A typical solution: first, calculate the proportion of students in each year group. Multiply that proportion by 50 to determine the sample size for each year. Then use simple random sampling within each year group, for instance by assigning numbers and using a random number generator.
示例： “校长想从学校 800 名学生中调查 50 名。描述如何按年级分层抽样。” 典型解法：先计算各年级学生比例，将比例乘以 50 得到各年级样本量，然后在每个年级内使用简单随机抽样，例如编号后使用随机数生成器。
Common errors include forgetting to take proportional representation or using a convenience sample instead of a random method. Remember to mention how randomness is achieved and that every member of the population has a known chance of selection.
常见错误包括忘记按比例抽取或使用便利样本代替随机方法。务必提及如何实现随机性，并确保总体中每个成员有已知的被选机会。
3. Frequency Tables and Bar Charts | 频数表与条形图
Many past-paper tasks require you to complete a frequency table, draw a bar chart, or interpret the chart. You need to use the frequency density correctly if class intervals are unequal, though equal widths are common at Year 9.
许多真题要求你补全频数表、绘制条形图或解读图表。若组距不相等需正确使用频数密度，但 Year 9 通常为等宽组距。
Consider this table showing favourite colours from a survey of 30 students: Red 8, Blue 10, Green 6, Yellow 4, Other 2. To draw a bar chart, label both axes clearly, use equal bar widths, and leave gaps between bars. The vertical axis must be scaled appropriately and numbered.
考虑此表，30 名学生最喜欢颜色的调查结果：红 8，蓝 10，绿 6，黄 4，其他 2。绘制条形图时，清晰标记两轴，使用等宽条形，条形之间留间隙。纵轴须合理设标尺并标注数字。
Marks are lost for missing axis labels, inconsistent scale, or failing to use a ruler. Always give the chart a title. When reading data from a bar chart, check the scale carefully to avoid miscounting.
因缺少轴标签、刻度不一致或不用直尺而失分。务必给图表加标题。从条形图读取数据时，仔细检查刻度以防数错。
4. Pie Charts | 饼图
Drawing and interpreting pie charts is a regular feature. You must calculate the angle for each category using the formula: Angle = (Frequency ÷ Total frequency) × 360°. Use a protractor accurately and label each sector or add a key.
绘制和解读饼图是常见内容。必须使用公式计算每类的角度：角度 =（频数 ÷ 总频数）× 360°。准确使用量角器并标注各扇区或添加图例。
Example: “A student spends £60 a month: £15 on sweets, £25 on music, £10 on games, and £10 on other items. Draw a pie chart.” Angles: Sweets 90°, Music 150°, Games 60°, Other 60°. In the exam, you can earn marks for showing calculations and then drawing the angles within 2°.
示例： “一名学生每月花费 60 英镑：糖果 15 英镑，音乐 25 英镑，游戏 10 英镑，其他 10 英镑。绘制饼图。” 角度：糖果 90°，音乐 150°，游戏 60°，其他 60°。考试中写出计算过程并将角度精确至 2° 以内即可得分。
A common pitfall is confusing the frequency with the angle, or forgetting to check that the angles sum to 360°. When interpreting a pie chart, avoid assuming that equal areas mean equal actual values unless the total frequency is known.
常见误区是混淆频数与角度，或忘记检查角度之和为 360°。解读饼图时，除非已知总数，否则不能因为面积相等就认定实际数值也相等。
5. Scatter Graphs and Correlation | 散点图与相关性
WJEC papers frequently ask you to plot a scatter graph, describe the correlation, and draw a line of best fit. Correlation is described as positive, negative, or zero (no correlation). The line of best fit should pass through the middle of the points with roughly equal numbers above and below.
WJEC 试卷常要求绘制散点图、描述相关性并画出最佳拟合线。相关性被描述为正相关、负相关或零相关（无相关）。最佳拟合线应通过点群中央，线上下的点数大致相等。
Sample task: “Plot the data on a scatter graph. Draw a line of best fit. Use your line to estimate the test score if a student studied for 5 hours.” Make sure to plot points as small crosses, not dots. When estimating, read from the line of best fit, not from the nearest point.
样题： “在散点图上绘制数据。画出最佳拟合线。利用所画直线，估计学习 5 小时的学生可能获得的考试分数。” 务必用小叉号描点，不用圆点。估计时，从最佳拟合线读取，而非最邻近点。
You should comment on the strength of the correlation (strong, moderate, weak). Avoid extrapolating far beyond the data range, as the relationship may not hold there.
应评价相关的强弱（强、中等、弱）。避免远超出数据范围的预测，因为该范围内关系可能不成立。
6. Mean, Median, Mode and Range | 平均数、中位数、众数和范围
Calculating measures of central tendency and spread is essential. You should be able to find the mean from a list or a frequency table, identify the mode, and determine the median and range.
计算集中趋势和离散度指标是必考内容。应能从简单数据列或频数表中求平均数，识别众数，并确定中位数和范围。
For a simple list: 5, 7, 9, 12, 12, 15, the mean is (5+7+9+12+12+15)÷6 = 10, mode is 12, median is 10.5, range is 15−5 = 10. For a frequency table, multiply each value by its frequency, sum the results, and divide by the total frequency.
对于简单数据：5, 7, 9, 12, 12, 15，平均数为 (5+7+9+12+12+15)÷6 = 10，众数为 12，中位数为 10.5，范围为 15−5 = 10。对于频数表，用各值乘以频数，求和后再除以总频数。
The median position is found using (n+1)/2. If you have grouped data without exact values, use midpoints for the mean calculation. Exam questions often ask which average best represents the data; consider the effect of outliers.
中位数位置用 (n+1)/2 确定。若为缺少精确值的分组数据，使用组中点来计算平均数。考试常问哪种平均数最能代表数据，应考虑极端值的影响。
7. Stem-and-Leaf Diagrams | 茎叶图
Stem-and-leaf diagrams are a common Year 9 topic. You must sort leaves in ascending order, provide a key, and then find the median, mode, and range directly from the diagram.
茎叶图是 Year 9 常见主题。必须将叶按升序排列，提供图例，然后直接从图中找出中位数、众数和范围。
Example data: 12, 15, 21, 21, 23, 34, 37. Stem 1: leaf 2,5; Stem 2: leaf 1,1,3; Stem 3: leaf 4,7. Key: 1|2 means 12. The median is the 4th value (21), mode is 21, range is 37−12 = 25.
示例数据： 12, 15, 21, 21, 23, 34, 37。茎 1：叶 2,5；茎 2：叶 1,1,3；茎 3：叶 4,7。图例：1|2 表示 12。中位数为第 4 个值（21），众数为 21，范围为 37−12 = 25。
A frequent mistake is forgetting to include the key, which causes loss of the mark for interpretation. Also, you must order the leaves; an unordered diagram is not accepted.
常见错误是忘记写图例，这会导致解读题失分。此外，叶必须排序，未排序的图不被接受。
8. Basic Probability | 概率基础
Probability questions often involve spinners, dice, or picking coloured counters. The probability of an event is (number of favourable outcomes) / (total number of possible outcomes), expressed as a fraction, decimal, or percentage.
概率题常涉及转盘、骰子或抽取彩色筹码。事件的概率 =（有利结果数）/（所有可能结果总数），用分数、小数或百分数表示。
Example: “A bag contains 4 red, 3 blue and 5 green counters. One counter is taken at random. What is the probability it is blue?” Total counters = 12, P(blue) = 3/12 = 1/4. What is the probability it is not red? P(not red) = 1 − 4/12 = 8/12 = 2/3.
示例： “袋中有 4 红、3 蓝和 5 绿筹码。随机取一枚，它是蓝色的概率是多少？” 总数 12，P(蓝) = 3/12 = 1/4。它不是红色的概率是多少？P(非红) = 1 − 4/12 = 8/12 = 2/3。
Emphasise that probabilities must lie between 0 and 1. An event that is certain has probability 1, and an impossible event has probability 0. In WJEC, you are often asked to work with probability on a probability scale marked from 0 to 1.
须强调概率值必须介于 0 至 1 之间。必然事件概率为 1，不可能事件概率为 0。WJEC 常要求你在标有 0 到 1 的概率刻度上标出事件。
9. Sample Space Diagrams and Tree Diagrams | 可能性空间图与树状图
When two events happen together, a sample space diagram (two-way table) lists all possible outcomes. For example, rolling two dice: the table shows 36 outcomes. You can then count the number of outcomes that give a certain sum.
当两事件同时发生时，可能性空间图（双向表）列出所有可能结果。例如，掷两个骰子：表格显示 36 种结果。你可以从中数出得到特定和的可能结果数。
Tree diagrams are used for sequential events. Label branches with probabilities. Multiply along branches for combined probability. For independent events, probabilities on the second set of branches are the same regardless of the first outcome.
树状图用于序贯事件。用概率标注分支，沿分支相乘求联合概率。对于独立事件，第二层分支的概率不受首层结果影响。
Example: “The probability it rains on a day is 0.3. Draw a tree diagram for two days. Find the probability it rains on both days.” Rains (R) 0.3, No rain (N) 0.7. P(R,R) = 0.3 × 0.3 = 0.09. Ensure probabilities on each pair of branches sum to 1.
示例： “某天下雨的概率为 0.3。画出连续两天的树状图。求两天都下雨的概率。” 下雨 (R) 0.3，不下 (N) 0.7。P(R,R) = 0.3 × 0.3 = 0.09。确保每组分支概率之和为 1。
Common mistakes include adding instead of multiplying, or forgetting to update probabilities when events are not independent (conditional probability, which may be introduced at this level). Always read the question carefully to check whether replacement occurs.
常见错误包括用加代替乘，或在非独立事件（条件概率，此阶段或会引入）中忘记更新概率。务必仔细读题，判断是否存在放回。
10. Comparing Distributions | 比较分布
A typical past-paper question provides two sets of data, such as test scores from two classes. You are asked to compare them using averages and the range. Make a comment about central tendency (compare means or medians) and spread (compare ranges or interquartile ranges).
典型的真题给出两组数据，如两个班级的考试成绩。要求你使用平均数和范围进行比较。需对集中趋势（比较平均数或中位数）和离散度（比较范围或四分位距）做出评论。
Example: Class A: mean = 65, range = 22. Class B: mean = 70, range = 10. Compare: Class B has a higher mean score, so on average they performed better. Class A has a larger range, meaning scores were more spread out and less consistent than Class B.
示例： A 班：平均分 65，范围 22。B 班：平均分 70，范围 10。比较：B 班平均分更高，因此整体表现更好。A 班范围更大，意味着分数更分散、一致性低于 B 班。
You must write your comparison in context, using words like ‘on average’ and ‘more consistent’. Simply stating the numbers without comparison will not gain full marks. If box plots are provided, compare medians and interquartile ranges.
必须在具体语境中写出比较，使用诸如“平均而言”和“更一致”等词语。只罗列数字而不进行比较无法获得全分。若给出箱线图，则比较中位数和四分位距。
Published by TutorHao | Statistics Revision Series | aleveler.com
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